Billionaire trading agitator Carl Icahn today reported that he had, as promised, had dinner with Apple CEO Tim Cook last night, when he lobbied for a $150 billion stock buyback program, a 150% increase over the company's current plan.

"Had a cordial dinner with Tim last night. We pushed hard for a $150 billion buyback. We decided to continue dialogue in about three weeks," Icahn said via Twitter today.

Apple shares were up 2.6% in trading Tuesday, pushing close to $489 a share by 1 p.m. ET.

It was the fourth time in the last six weeks that Icahn, known as a corporate activist, tweeted to announce dealings with Apple. On Aug. 13, Icahn revealed that he had acquired "a large position" in Apple, that he believed the stock to be undervalued and that he had spoken with Cook about an increase in the company's already-under way buyback initiative.

Ten days later, he again turned to Twitter to say he had lined up dinner with Cook and would be pressing the CEO on stock buybacks.

"The gift that keeps on giving," said Patrick Moorhead, principal analyst with Moor Insights & Strategy, in an email Tuesday, referring to his earlier-expressed belief that Icahn's interest in Apple would be long, involved and at the very least, a major distraction for Cook.

Icahn typically buys a stake in a company to demand management changes and advocate the use of cash reserves to boost the share price, including paying higher dividends or buying back shares. The latter is Icahn's strategy with Apple.

Icahn has not revealed the exact size of his holdings. In filings with the U.S. Securities and Exchange Commission (SEC) for the quarter ending June 30, the one most recently reported, Icahn said he owned no Apple stock, meaning that his purchases began on or after July 1. Icahn will be required to disclose his holdings for the third quarter, so his holdings will be public some time this month.

Apple already is in the middle of an aggressive share buyback program. Last year, Apple said it would use $10 billion to fund buybacks that would retire shares and thus increase the value of those still remaining. In April, the Cupertino, Calif., company increased the buyback program to $60 billion, which is to be spent through 2015.

Icahn, however, wants even more spent on buybacks and has suggested that if Apple borrowed to do so, it could retire enough shares to boost the price above $700, or where it was more than a year ago before taking a plunge as investors worried about the lack of new products and questioned the company's commitment to growth.

Apple has a huge pile of cash: At the close of the quarter that ended June 30, it reported nearly $147 billion in cash, securities and other investments. Most of that, however, was banked overseas. Apple has resisted calls to repatriate it to the U.S. because it would have to pay taxes on those monies.

In fact, Apple borrowed some of the money it will use on its current buyback arrangement.

Icahn played a major role in opposing Michael Dell's bid to privatize the PC maker that carries his name. In early September, however, Icahn and his associates tossed in the white towel, even as he claimed his opposition prompted Michael Dell and his investors to bump up the price they'd pay for each share.